English

A diagrammatic categorification of the q-Schur algebra

Quantum Algebra 2012-02-08 v3

Abstract

In this paper we categorify the q-Schur algebra S(n,d) as a quotient of Khovanov and Lauda's diagrammatic 2-category U(sln). We also show that our 2-category contains Soergel's monoidal category of bimodules of type A, which categorifies the Hecke algebra H(d), as a full sub-2-category if d does not exceed n. For the latter result we use Elias and Khovanov's diagrammatic presentation of Soergel's monoidal category of type A.

Keywords

Cite

@article{arxiv.1008.1348,
  title  = {A diagrammatic categorification of the q-Schur algebra},
  author = {Marco Mackaay and Marko Stosic and Pedro Vaz},
  journal= {arXiv preprint arXiv:1008.1348},
  year   = {2012}
}

Comments

60 pages, lots of figures. v3: Substantial changes. To appear in Quantum Topology